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Recent Courses
Past Courses
- Math 731 Topics in Algebraic Geometry: F-Singularities in Commutative Algebra and Algebraic Geometry Fall 2022
- Math 217 Linear Algebra. Course Coordinator (multiple sections) Fall 22 & Winter 23 (all in Canvas nowadays, but similar to Winter 2017)
- Math 592, Algebraic Topology Winter 2020
- Math 614, Commutative Algebra, Fall 2019
- Math 700: Reading course from Math 732 notes, Fall 2019
- Math 732, Characteristic p methods in commutative algebra and algebraic geometry, Winter 2019
- Math 412: Undergraduate Abstract Algebra, Fall 2018 and the previous year Fall 2017
- Math 217: Linear Algebra Winter 2017, Winter 2016 and Fall 2015 Also Fall 20, Fall 22, Winter 23 (canvas)
- MatS535 Resolution of Singularities at the University of Jyvaskyla Summer School 2016
- Algebra 2 An introduction to field theory and Galois theory.
University of Jyvaskyla, Finland. Fall Semester 2016
- Math 594: Graduate Algebra II, Winter 2015
- Math 593: Graduate Algebra I, Fall 2014
- Math 115: Calculus I, UM, winter 2014. First semester calculus!
- Math 631: Algebraic Geometry I UM Fall 2013
- Math 632: Algebraic Geometry II, UM Winter 2013
- Math 631: Introduction to Algebraic Geometry University of Michigan, Fall 2012
- Math 513: Honors Algebra II University of Michigan, Winter 2012
- Math 512: Honors Algebra I, University of Michigan, Fall 2011
- Math 296: Honors Mathematics II, University of Michigan, Winter 2011
Abstract Linear Algebra.
- Math 295: Honors Mathematics I, University of Michigan, Fall 2010
Delta-epsilon calculus using Spivak’s calculus book with additional topics (notably topology and metric spaces) mixed in.
- A Novice’s Road Map of Research Trends in Contemporary Algebraic Geometry, short course at the University of Helsinki, May 2010.
Problem Set for students taking the course for credit.
- MatS 138: Undergraduate Representation Theory (winter 2010) Jyvaskylan Yliopisto
Plus an exercise session run by Lauri Kahanpaa
- Math 412: Introduction to Modern Algebra (fall 2009).
Text: Hungerford’s undergrad book.
- Math 632: Introduction to Algebraic Geometry II: Schemes (winter 2009)
Main Text: Hartshorne, Algebraic Geometry
Supplementary Write-up on pullbacks and all that
- Math 631: Intro to Algebraic Geometry; Fall 2008
- Math 385: Math for Elementary School Teachers; winter 2007
Main Text: Parker and Baldridge, “Elementary Mathematics for Teachers”, supplemented by the Singapore Primary mathematics texbooks 3A, 4A, 5A, 6A and workbook 5A.
(These are sold in the local bookstores bundled together in one package, with the main textbook).
Course description: Follow link to Math 385 from Math course catalog
- Math 631: Introduction to algebraic geometry. Fall 2006.
- Math 732, Topics in Algebraic Geometry: Rational and Nearly Rational Varieties. Winter 2006.
This was an intermediate level introduction to the study of projective varieties that share some of the birational features of projective space. Topics discussed included: rationality of surfaces and Castelnuovo’s criterion (with lots of basic background material on surfaces following Beauville’s book), rationality of varieties over non-algebraically closed fields, the Noether-Fano equations, superridigity and non-rationality of quartic threefolds, maximal centers, discrepancies, singularities of pairs, multiplier ideals, inversion of adjunction. A little bit on rationally connected varieties.
Texts: Beauville’s Complex Algebraic Surfaces and Koll\’ar, Smith, Corti, “Rational and Nearly Rational Varieties”.
- Math 593, Algebra I. Fall 2005.
This is the first year graduate level algebra course (“alpha course”). Here is the standard department Math 593 Syllabus; though I usually cover quite a few topics not on it, mostly basic commutative and homological algebra.
Problem Sets;
Exam I, with solutions;
Exam II, with solutions;
Final Exam, with solutions
- Math 632: Schemes and cohomology of sheaves, Winter 2002, Winter 1997 (Michigan)
Math 632 Course Description
Supplementary Write-up on pullbacks and all that
- Math 631: Introduction to Algebraic Geometry, Fall 1996, 2001, 2006 (Michigan) Text: Shafarevich, vol I. Old Problem Sets.
- Introduction to Algebraic Geometry, University of Jyvaskyla, Winter 2001
Text: An invitation to Algebraic Geometry, by Smith, Kahapaa, Kekalainen, Traves (Springer)
- Math 115: Calculus I, Section 12, Fall 2000
The official Math department Math 115 website
(Caution: the department is not very quick about updating information here. )
- Math 105: Functions, Data, Graphs, Winter 2000
- Math 614 : Commutative Algebra, University of Michigan, Fall 1999
- Math 513: Linear Algebra, University if Michigan, Winter 1999
Supplementary Write up: Bases for Infinite Dimensional Vector Spaces
- Honors Calculus (18.014) at MIT, Fall 1997
- Graduate student seminar on Tight Closure, Fall 1997 MIT
- Graduate reading course on Basic Algebra (following Lang’s book), Fall 1997, MIT
- Intersection Theory: University of Michigan, Winter 97
Summary of main points covered in the graduate student intersection theory seminar
- Math 631 (Intro to Algebraic Geometry), and Introduction to Commutative Algebra (Reading Course) University of Michigan, Fall 1996
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